# International environmental agreements under uncertainty.

1. IntroductionEnvironmental issues such as climate change, the depletion of the ozone layer, acid rain, deforestation, and biological diversity have come to the forefront of public concern in recent years, and have focused the attention of policy makers. Environmental issues have an intrinsically trans-national, or global dimension, in which the actions of one party will affect the welfare of other interested parties. However, in the absence of a supra-national body which can issue and enforce directives on environmental policy, the potential gains from policy coordination are limited by the willing participation of diverse, and self-interested sovereign countries.

The emergence of international environmental agreements as a means towards achieving this coordination can be seen in this light. Although such agreements have historical precedents, their role has become much more prominent in the last decade or so, in particular with the Montreal Protocol on the ozone layer (and its subsequent amendments strengthening its provisions), and the Rio Convention on climate change. The incentives underlying international environmental agreements have been analysed in terms of coalition formation among self-interested players using game-theoretic tools. Examples of recent papers include Barrett (1994), Carraro and Siniscalco (1993, 1994), Chander and Tulkens (1992), Heal (1994), and Sandler (1996). The starting point of these papers is to postulate a set of payoff functions for individual countries motivated by the externalities inherent in global environmental policy, and then to analyse the payoffs which accrue to groups of countries which act to maximize the coalition's payoff. The incentives to join a coalition are then analysed in terms of the difference in the payoff to an individual country inside and outside the coalition.

Although the existing literature has generated numerous insights into the problem of international environmental agreements, it has been limited in a number of respects. First, the analysis has largely been conducted under the assumption of symmetry of the interested parties. This may not be the most promising approach to examining the strategic incentives generated by differential gains and losses across jurisdictions. A related feature is perfect information. This runs counter to the acknowledged uncertainties underlying global environmental issues and the disparities between countries.

In some instances, uncertainty may not be an overriding concern. In this respect, it is illuminating to distinguish the different types of environmental externality.(1) For acid rain and deforestation, the problem is largely one of coordinating the actions of an interlocking set of local parties. The curbing of deforestation, for instance, yields private goods, country-specific public goods, and global public goods (Sandler, 1993), and the bargaining takes account of this mix. For such problems, any uncertainty there is plays a relatively small role, and the focus of the bargaining is on the sharing of the potential surplus to coordination. In the case of ozone depletion, it could be argued that much of the uncertainty concerning its likely effects had been resolved before the signing of the Montreal Convention. Indeed, Murdoch and Sandler (1997) argue that the support for the Montreal Convention was due to the fact that it codified reductions in CFC emissions that polluters were voluntarily prepared to accomplish as the scientific evidence came in. In this case, also, uncertainty seems to have played only a marginal role.(2)

However, the same is not true with regard to the greenhouse effect and the related question of global climate change.(3) There are two dimensions to the uncertainties associated with global warming. First, at an aggregate level, there is uncertainty concerning the broad impact of increased carbon dioxide emissions on the increase of average temperature over the globe and the likely effects thereof. Second, and more importantly, there is uncertainty concerning the distribution of the damage caused by carbon dioxide emissions as a result of localized climate change, and hence uncertainty concerning the distribution of the benefit to curtailing carbon dioxide emissions.

At an aggregate level, several estimates have been reported of the global economic costs of the greenhouse effect, for example, Nordhaus (1991), Cline (1992), and Fankhauser (1993). However, the differential impact of global warming across geographical regions of the world is less well understood. Climatologists raise the spectre of shifting currents which may turn Europe into Alaska, of the drying up of grain belts into deserts, of great rivers drying up as a result of the disappearance of ice packs, and of the northward migration of old and new tropical pests and diseases. In short, the likelihood of catastrophic surprises due to global warming is much harder to predict than the mere increase in average temperatures.(4) For the British Isles, and northern Europe in general, global warming may not translate into a general increase in temperature, since the current climate is dependent on the prevailing currents, and such currents may be disrupted by global warming. Formal models of climate give some indication of the effects, but they are subject to the usual limitations. Thus, even if a consensus emerged as to the average impact of global warming, the uncertainty concerning regional variations is unlikely to dissipate, and this will affect the incentives of countries to join an environmental coalition in subtle and complex ways.

The main contribution of our paper is to re-examine the issue of international environmental agreements in a context (such as global warming) in which there is uncertainty concerning the distribution of the benefits of pollution abatement activity, and when countries are not identical. We analyse a game of coalition formation among three countries. The payoffs of all three countries are increasing in the aggregate pollution abatement, but the marginal benefit of aggregate abatement to an individual country is uncertain.

Within this framework, it is possible to address two important issues. First, when disparate countries are negotiating to form coalitions, what determines the membership of such coalitions? Second, what is the value (if any) of delaying environmental negotiations until better scientific information is available? The answer to the first question turns out to be that coalitions are more likely to form between countries which are similar. The second question is examined by comparing two scenarios of negotiations. In the first, negotiations take place before the uncertainty is resolved, and abatement levels are chosen in anticipation of learning the true values of abatement. In the second, the countries negotiate after the uncertainty is resolved, and only then decide on their strategies concerning coalition formation and abatement levels.

These two scenarios are formalized in terms of two distinct extensive form games based on the same fundamentals, where the differing rules of the two games capture the distinction between negotiating under uncertainty and negotiating after uncertainty has been resolved. In the first, nature's move in determining the benefit of abatement activity comes after the moves of the individual countries, and the ex ante payoff of an individual country is calculated by taking expectations over the possible choices of nature at the final stage. In the second game, nature moves before the individual countries. Thus, when the countries begin their negotiations for coalition formation, they are in full possession of the information concerning the value of abatement activity. For each outcome of nature's chance move, there corresponds a profile of equilibrium actions of the three countries, including the decisions on whether to join a coalition or not. Under this second scenario, the actions of individual countries are functions of the underlying state of nature, and therefore are random variables themselves. The ex ante payoff of an individual country is then obtained by taking the expected value of these final payoffs. By comparing the ex ante payoffs under the two scenarios, we may address the question of whether the countries are better off (in ex ante terms) to have ex ante negotiations or to delay negotiations until the uncertainty has been resolved.

The value of information in environmental policy has been discussed in the context of a two country model by Ulph and Ulph (1994a) and by Ulph and Maddison (1995). Although the issue of coalition formation cannot be addressed adequately in a two country model, these papers are able to demonstrate that the value of information in strategic situations can be negative, depending on the uncertainty structure underlying the game. These papers assume the strategic substitutability of pollution abatement. In our model, we do not need this assumption, and we regard this as a virtue of our model, as we explain below. If, indeed, there is strategic substitutability of abatement activity, our conclusions are strengthened.

To gain an intuition for our main results, it is instructive to contrast the role of uncertainty in a single-person decision problem from that in a strategic situation. In a one-person decision problem, the value of information can never be negative, since it is open to the decision maker to ignore any information. In general, a decision maker can do strictly better by utilizing the information concerning the state of nature. However, in strategic situations, this need not hold. In our case, there is a trade-off. On the one hand, information concerning the state of nature helps the decision makers by allowing them to take more informed decisions. However, it is also the case that cooperation is more difficult to achieve when the likely winners and losers are known when negotiation takes place. In our case, the outcome when more information is available is less efficient in terms of total payoffs than the corresponding welfare benchmark when negotiations take place in ignorance.

This argument relies on a very different mechanism from those which invoke the option value of abatement activity, arising from the fact that changes to the stocks of greenhouse gases take long periods of time to achieve (Chichilnisky and Heal, 1993; Ulph and Ulph 1994b). The validity of such arguments on the advantages to flexibility will serve to reinforce the mechanism involved in our paper.

2. A three country model

Our model describes the interactions between three countries, indexed by the set {1, 2, 3}. We denote by [y.sub.i] the level of pollution abatement undertaken by country i. The payoff of country i consists of the total benefit derived from total pollution abatement by all countries, minus the cost of abatement activity of its own abatement activity. In particular, we define the final payoff of country i as

[Mathematical Expression Omitted] (1)

We note that we do not impose the strategic substitutability of abatement levels. We believe this to be a virtue of our model, since for the case of greenhouse gas emissions, the degree of such substitutability, if any, is likely to be small.(5) The marginal benefit of aggregate abatement, [[Theta].sub.i], is a random variable which takes values in the set

{[z.sub.1], [z.sub.2], [z.sub.3]} (2)

where each [z.sub.k] is a positive number, and [z.sub.1] [less than] [z.sub.2] [less than] [z.sub.3]. The realizations of the set of random variables {[[Theta].sub.i]} is determined by nature in the following sequence of experiments. First, nature selects one of the three countries with uniform probability of 1/3. If country i is drawn, then nature sets [[Theta].sub.i] = [z.sub.3]. In other words, country i is given the highest marginal benefit of total abatement. Next, of the two remaining countries (excluding i), nature chooses a country with equal probability of 1/2. If country j is chosen at this stage, then nature sets [[Theta].sub.j] = [z.sub.2]. In other words, country j is given the second largest marginal benefit of abatement activity. For the last remaining country (called k), nature sets the realization of [[Theta].sub.k] to [z.sub.1]. This country has the lowest marginal benefit of abatement activity.

By construction, each [[Theta].sub.i] is identically distributed over the set {[z.sub.1], [z.sub.2], [z.sub.3]}, and each outcome has probability 1/3. The expected payoff of country i in its general form is given by

[Mathematical Expression Omitted] (3)

where the expectation is taken over the joint distribution over the set of random variables {[[Theta].sub.i]}. Each country aims to maximize this expected payoff within the particular rules of the game. We consider two sets of rules. In the first, the countries decide on their abatement levels before the uncertainty concerning {[[Theta].sub.i]} is resolved. In the second, countries choose abatement after they learn the outcome of nature's experiment. An important element of the countries' decisions is the possibility of forming coalitions before choosing their abatement levels.

If a country is a member of a coalition C, it is constrained to maximize the sum of payoffs of all countries in C. A country which is not a member of a coalition chooses its abatement level to maximize its own individual payoff, without regard to the payoffs of the other countries. The payoffs of all countries (whether in a coalition or not) is then derived from the underlying payoffs of the non-cooperative game - that is, from (1). If the coalition consists of all three countries, we call this the grand coalition. If the coalition consists of two countries, we shall refer to this as a partial coalition.

The stability of a coalitional structure is determined by the self-interested membership decisions of all countries. Since there are just three countries, it is without loss of generality to consider at most one coalition in existence. Informally, we can say that a coalition C is stable if, first, no country in C can do better by leaving C and acting individualistically, and second, no country outside C can do better by joining the members of C to form an enlarged coalition. Three coalitional structures may emerge - namely, the grand coalition, a partial coalition, or the individualistic outcome, in which there is non-trivial coalition. More formally, if we denote by [[Pi].sub.i](C) the payoff of country i when it is a member of the coalition consisting of the set C of countries, and denote by [[Pi].sub.i]({i}) the corresponding payoff of country i when it acts individualistically (in the trivial coalition {i}), we say that a coalition C is stable if

[[Pi].sub.i](C) [greater than or equal to] [[Pi].sub.i] ({i}) for all countries i [element of] C (4)

[[Pi].sub.j] (C [union] {j}) [less than] [[Pi].sub.j] ({j}) for all countries j [not an element of] C (5)

If such a coalition exists, then no existing member prefers to leave it, and no outsider wants to join it. Notice that, according to our definition of stability, if a country is indifferent between joining a coalition and staying outside it, it will decide to join.

If a coalition forms before the uncertainty concerning {[[Theta].sub.i]} is resolved, then the payoff [[Pi].sub.i] refers to the expected payoff of country i, while if a coalition forms after the random variables {[[Theta].sub.i]} are realized, it refers to the ex post payoff [[Pi].sub.i] given by (1).

Having described the framework and the questions to be posed, we proceed to analyse the outcome under our two scenarios. We first start with the case of coalition formation before the uncertainty is resolved. We shall call this the case of ex ante negotiation.

3. Equilibrium with ex ante negotiation

Under this scenario, the countries negotiate before learning the true value of the benefit of aggregate pollution abatement. Thus, in (3) the pollution abatement levels must be chosen before the realizations of {[[Theta].sub.i]} are known, so that the {[y.sub.i]} are non-random. Thus, (3) takes the form

[Mathematical Expression Omitted] (6)

Suppose that C is a coalition which does not include i. Let us consider the optimal abatement level of country i for two cases: when it is outside the coalition C, and when it joins the countries in C to form the enlarged coalition C [union] {i}. If country i is outside the coalition, its optimal abatement level is

[y.sub.i] = E([[Theta].sub.i]) (7)

On the other hand, if i is a member of the coalition C [union] {i}, its abatement level is chosen to maximize [summation over k [element of] C [union] {i}] E([[Pi].sub.k]). From (6), this maximand can be written as

[Mathematical Expression Omitted] (8)

so that the optimal abatement level of country i which joins the countries in coalition C is given by

[y.sub.i] = [summation over k [element of] C [union] {i}] E([[Theta].sub.k]) (9)

By substituting the optimal abatement levels into (6), we can compare the expected payoff for country i for when it stays outside the coalition C, and for when it joins the countries in C to form the enlarged coalition C [union] {i}.

Suppose country i stays outside the coalition, and denote by [Mathematical Expression Omitted] the number of countries in C. Since each country k [element of] C chooses abatement level [Mathematical Expression Omitted], country i's expected payoff is

[Mathematical Expression Omitted] (10)

On the other hand, if country i joins the countries in C to form the enlarged coalition C [union] {i}, then its expected payoff is

[Mathematical Expression Omitted] (11)

The payoff difference between (11) and (10) then represents the incentive for country i to join the countries in C to form the enlarged coalition C [union] {i}. Let us denote this payoff difference by [[Delta].sub.A](i, C). The notation indicates that it is the incentive for country i to join coalition C when there is ex ante negotiation. By cancelling out common terms

[Mathematical Expression Omitted]

Thus, ruling out the trivial case of an empty C, we have [[Delta].sub.A](i, C) [greater than or equal to] 0 if and only if

[Mathematical Expression Omitted] (12)

This condition has a simple interpretation. The expression inside the brackets on the right-hand side is the average of the ex ante expected values of [[Theta].sub.k] for the members of C. Since the [[Theta].sub.k] are identically distributed, we have [Mathematical Expression Omitted], for all i and j, where [Mathematical Expression Omitted]. Thus, provided that [Mathematical Expression Omitted], which is guaranteed by our assumptions, we can divide by [Mathematical Expression Omitted] so that (12) is reduced to the condition that [Mathematical Expression Omitted]. In other words, any country has an incentive to join an existing coalition of size 2. From eqs (4) and (5), a country will join a coalition if it is indifferent between joining and not joining, so that the grand coalition consisting of all three countries is stable under the scenario of ex ante negotiations. Moreover, the grand coalition is the only stable coalitional structure, since if the coalition consists of fewer than three countries, a country outside the coalition prefers to join, rather than to stay out. Let us summarize this conclusion in terms of the following lemma.

Lemma 1 With ex ante negotiation, the grand coalition is the uniquely stable coalition structure.

From this conclusion, we can now specify the equilibrium payoffs of the three countries. In the grand coalition, the abatement level of each country is given by [y.sub.i] = 3E([[Theta].sub.i]). Thus, substituting into eq. (6), the ex ante expected payoff of country i is E([[Pi].sub.i]) = 3E([[Theta].sub.i]) [summation of] E([[Theta].sub.k]) where k = 1 to 3 - [[(3E([[Theta].sub.i])).sup.2]/2], so that

[Mathematical Expression Omitted]

4. Equilibrium with ex post negotiation

Under our second scenario, coalition formation and pollution abatement takes place after the realizations of the random variables {[[Theta].sub.i]} are known. Thus, the abatement levels {[y.sub.i]} are functions of {[[Theta].sub.i]}, and hence are, themselves, random variable. The ex post payoff of country i given a coalition C of countries is given by

[Mathematical Expression Omitted] (14)

Let us compare the optimal abatement level of country i under two cases: when it is outside the coalition C, and when it joins the countries in C to form the enlarged coalition C [union] {i}. If country i is outside the coalition C, its optimal abatement level is

[y.sub.i] = [[Theta].sub.i] (15)

If i is a member of the coalition C [union] {i}, its abatement level is chosen to maximize [summation over k [element of] C [union] {i}] [[Pi].sub.k]. Then, the optimal abatement level of country i who joins the countries in coalition C is given by

[y.sub.i] = [summation over k [element of] C [union] {i}] [[Theta].sub.k] (16)

By substituting the optimal abatement levels into (14), we can compare the payoff for country i for when it stays outside the coalition C, and for when it joins the countries in C to form the enlarged coalition C [union] {i}. When country i stays outside the coalition, its payoff is given by

[Mathematical Expression Omitted] (17)

where, as before, [Mathematical Expression Omitted] denotes the number of countries in the coalition C. If country i joins the countries in C to form the enlarged coalition C [union] {i}, then its payoff is

[Mathematical Expression Omitted] (18)

The difference in i's payoff between (18) and (17) then represents the incentive for country i to join the countries to C to form the enlarged coalition C [union] {i}. Let us denote this payoff difference by [[Delta].sub.P](i, C). This notation is analogous to that in the previous section, and indicates that it is the incentive for country i to join coalition C when there is ex post negotiation. By cancelling out common terms, this payoff difference can be shown to be

[Mathematical Expression Omitted]

Thus, [[Delta].sub.P](i, C) [greater than or equal to] 0 if and only if

[Mathematical Expression Omitted] (19)

In other words, country i has a positive incentive to join the coalition C if and only if, two times the square of [[Theta].sub.i] is no smaller than C times the square of the average [[Theta].sub.k] of the countries in the existing coalition. Among other things, this implies that any coalition which forms at the ex post stage consists of the countries with the highest realizations of [[Theta].sub.i].

In particular, we can be certain that the grand coalition is never a stable coalitional structure given our assumption that [z.sub.1] [less than] [z.sub.2] [less than] [z.sub.3]. To see this, consider the country which draws the lowest realization of [Theta] (i.e. the country i for which [[Theta].sub.i] = [z.sub.3]). In order for the grand coalition to be stable, the inequality (19) must hold when the coalition C consists of the countries which have drawn the two larger values of [Theta]. However, this is impossible since [z.sub.3] [less than] ([z.sub.1] + [z.sub.2])/2.

Having ruled out the grand coalition, we ask whether a partial coalition consisting of two of the three countries is stable. Since each [[Theta].sub.i] takes values in the set {[z.sub.1], [[z.sub.2], [z.sub.3]}, the coalitional structure which is implied by (19) depends on the relative magnitude of the two largest values, namely [z.sub.2] and [z.sub.3]. If 2[z.sub.2] [greater than or equal to] [z.sub.3], then (19) implies that the partial coalition involving the countries with the two highest realizations of [Theta] is stable, and is the only stable coalitional structure. However, if 2[z.sub.2] [less than] [z.sub.3] even the partial coalition of two countries is unstable, and the only stable outcome is the individualistic outcome in which each country chooses its Nash equilibrium level. Let us summarize these conclusions in terms of the following lemma.

Lemma 2 With ex post negotiation, the grand coalition is never a stable outcome. If 2[z.sub.2] [greater than or equal to] [z.sub.3], a partial coalition of two countries is the uniquely stable coalition structure, but if 2[z.sub.2] [less than] [z.sub.3], the only stable coalitional structure is the individualistic outcome.

By virtue of this lemma, we are able to characterize completely the ex post coalition formation game, and the corresponding ex post payoffs of the three countries. Then, by taking expectations over all possible realizations of [[Theta].sub.i], we can calculate the ex ante expected payoff of country i. The lemma suggests that we must do this for two separate cases - the first when the partial coalition is stable, and the second when only the individualisic outcome is stable.

4.1 Case of partial coalition (2[z.sub.2] [greater than or equal to] [z.sub.3])

In this case, the countries which have drawn the two highest realizations of [Theta] (namely, [z.sub.2] and [z.sub.3]) form a partial coalition, and choose identical abatement levels of [z.sub.2] + [z.sub.3]. The country which has drawn the value [z.sub.1] chooses abatement level [z.sub.1]. Thus, if we denote by [[Pi].sub.i] the ex post payoff of the country which has drawn the value [z.sub.i], these ex post payoffs are given by

[Mathematical Expression Omitted] (20)

[[Pi].sub.2] = [z.sub.2]([z.sub.1] + 2([z.sub.2] + [z.sub.3])) - 1/2 [([z.sub.2] + [z.sub.3]).sup.2] (21)

[[Pi].sub.3] = [z.sub.3]([z.sub.1] + 2([z.sub.1] + [z.sub.3])) - 1/2 [([z.sub.2] + [z.sub.3]).sup.2] (22)

In order to calculate the ex ante payoff of a firm i, we take expectations over all possible realizations of {[[Theta].sub.i]}. Since a country has equal probability of drawing a value of [Theta] from the set {[z.sub.1], [z.sub.2], [z.sub.3]}, the ex ante expected payoff of all countries is identical, and is given by ([[Pi].sub.1] + [[Pi].sub.2] + [[Pi].sub.3])/3. Thus, for any country i, E([[Pi].sub.i]) is given by [Mathematical Expression Omitted]. Simplifying this expression, we have

[Mathematical Expression Omitted] (23)

We can compare this ex ante payoff with that which results from ex ante negotiation given by eq. (13), to give us the payoff advantage of ex ante negotiations over ex post negotiation. Since the ex ante payoff to ex ante negotiation is [Mathematical Expression Omitted], the payoff advantage to ex ante negotiation is

[Mathematical Expression Omitted] (24)

demonstrating that ex ante negotiation is superior to ex post negotiation, even when a partial coalition is feasible. The precise magnitude of this superiority can be seen to be large if the numerical values of the two highest marginal benefits of abatement are large. In this case, the welfare loss resulting from ex post negotiation is very high.

4.2 Case of individualistic outcome (2[z.sub.2] [less than] [z.sub.3])

In this case, even a partial coalition is infeasible, and the only stable coalition structure is that of individualistic choice in the Nash equilibrium of the abatement game. Then, each country's ex post choice of abatement is the realized value of its marginal benefit of abatement, [Theta]. The country which draws the value [z.sub.i] chooses abatement level [z.sub.i]. Thus, using the same notation as above, the ex post payoffs of the three countries are given by

[Mathematical Expression Omitted] (25)

[Mathematical Expression Omitted] (26)

[Mathematical Expression Omitted] (27)

Hence, the ex ante expected payoff of any country i is given by

[Mathematical Expression Omitted] (28)

As we would expect, the ex ante payoff when no coalitions are possible is smaller than when a partial coalition is feasible. Moreover, the payoff advantage of ex ante negotiation is even greater when no coalitions form. The payoff advantage of ex ante negotiation then becomes

[Mathematical Expression Omitted] (29)

This term is closely related to the variance of [[Theta].sub.i], and suggests that the potential welfare loss resulting from ex post negotiations is greater when the disparities in the marginal benefits of abatement are larger.

Summarizing our discussion, we can state the main result of this paper.

Theorem For any country i, its ex ante payoff is strictly higher with ex ante negotiations than with ex post negotiations.

The simplicity of the uncertainty structure governing our game plays a large role in allowing us to obtain explicit solutions to the coalition formation games, and the resulting payoffs from these equilibria. There are, however, some general lessons from the analysis which would be applicable to more complex situations. One of the key planks of our argument has been the feature that coalitions are easier to form between countries which share similar characteristics. Hence, the size of a coalition depends on the degree of disparity among the negotiating countries. If negotiations are conducted among disparate countries, the resulting coalition is likely to be small. This intuition explains our main result. When negotiations take place before the uncertainty is resolved, the differences between the three countries is small. However, after the uncertainty has been resolved, the three countries are now disparate players, facing rather different incentives. More generally, the differences between the negotiating countries will be smaller in ex ante terms than in ex post terms, so that the general principle which favours coalition formation among countries which are similar will have the implication that coalitions are more likely to form before the resolution of uncertainty rather than after it. Since the overall loss of economic efficiency is directly mirrored in the extent of the failure to form the grand coalition, this leads to our general conclusion that ex ante negotiation is welfare enhancing.

5. Concluding remarks

In this paper, we have outlined a reason for why ex ante negotiations are superior to ex post negotiations, based on the strength of the incentives to form coalitions. We believe that this is a novel observation, and one which has implications for the conduct of the international negotiations currently in progress. There is an alternative argument for the superiority of ex ante negotiations which draws on the fact that pollution has many of the features of an irreversible action, so that the option value of ex ante abatement is positive (Chichilnisky and Heal, 1993; Ulph and Ulph, 1994b). Such an option value will serve to reinforce the superiority of ex ante negotiations. A fully fledged dynamic model which combines both features is a worthy subject of further study. It is hoped that future research will tackle these issues, and to inform empirical debate concerning the actual magnitudes involved.

Acknowledgements

We have benefited from the incisive comments of a refereee. We also thank Alistair Ulph for comments on an earlier version of this paper.

1 We are grateful to the referee for pointing out the important differences in these cases.

2 One qualification here has to do with mixed strategy equilibria. Sandler and Sargent (1995) show that mixed strategies may play a role in negotiations and, as such, will generate uncertainties for the players.

3 Morrisette et al. (1990) consider some of the lessons from previous agreements for negotiations on global warming.

4 Nordhaus (1993) presents the results of a survey of scientist' judgements concerning such catastrophic changes.

5 Carrro and Siniscalco (1994, pp. 14-15) conjecture that 'in most cases of trans-national or global pollution, the best-reply functions should be near-orthogonal, and that the emission reduction by some countries should not be offset by greater emissions elsewhere'.

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Author: | Na, Seong-lin; Shin, Hyun Song |
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Publication: | Oxford Economic Papers |

Date: | Apr 1, 1998 |

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